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AstroCappella: Doppler Shifting

Doppler Shifting on Earth

When you see a cop by the roadside writing somebody a speeding ticket, or
hear the clamor of a fire truck going by, you're probably not sparing much
thought for the expansion of the universe, or even the rotation of the
Galaxy. But in fact, all these things are connected. The policeman using
his or her radar or laser speed gun to enforce a traffic law is using the
same physical principle that scientists use to study the rotation and
motion of stars, the distance to the edge of the Milky Way galaxy, and
even learn important things about our entire universe. This physical
principle is called the DOPPLER SHIFT.

When the fire truck passes, the sound of its siren changes. The sound
waves emitted by the approaching fire truck are pushed closer together by
its motion, so the notes seem to have a higher frequency than they'd have
if you and the fire truck were both parked. In the same way, the sound
waves from a receding fire truck are appear to have a lower frequency. The
cop waiting by the roadside with his speed gun uses the same physical
effect; he bounces a radar wave off your car and measures the frequency of
the reflected wave. The frequency will be higher the faster you're going.
Better not be going too fast, because the policeman can measure your speed
to a fraction of a mile per hour using this method - probably more
accurately than your speedometer, in fact.

Johann Christian Doppler (1803-1853) first demonstrated the effect using
sound waves. But we see a similar effect with light waves. On Earth the
effect is so tiny that we normally don't notice it. But when we study the
stars, we can get a lot of mileage out of the Doppler Effect.

From Earth to Moon

We can bounce radar waves off the Moon and the nearby planets in the same
way as we can bounce them off a car. The development of radar during World
War II allowed scientists to accurately determine the distance to the Moon
by measuring the time delay required for a radio signal to return to the
Earth. Nowadays, using laser ranging, we can measure distances to the Moon
to within an error of 3 cm, and make topographic profiles of lunar craters
and mountains without even going there.

At 240,000 miles, the Moon is close enough for us to make active
measurements. But for most of astronomy the situation is different; we
can't experiment with a star (yet), or bounce radar off another galaxy
(because the power needed would be too great and the time it would take
for the wave to bounce back is too long), so scientists will make passive
measurements from afar, try to interpret what they see in the sky, and
make their theories. Further observations will then prove or disprove this
theory. Sometimes a theory may lead scientists to perform observations
they wouldn't otherwise think of. One example: Einstein's Theory of
Relativity predicts that light will bend when passing a sufficiently
massive object, and astronomer Arthur Eddington proved this during a solar
eclipse in 1919, by measuring the change in the apparent position of stars
whose light passed close to the edge of the Sun.

But let's get back to the DOPPLER EFFECT.

Redshifts, Blueshifts

Stars emit light. Using a prism or a diffraction grating, we can spread
this light out into a spectrum. If we look at the spectrum of the Sun or
any other star, we see not only the rainbow of colors from red, orange and
yellow through to violet, but also a distinctive pattern of dark lines. At
certain wavelengths, light will be ABSORBED by chemical elements like
hydrogen, helium, calcium, and iron. These wavelengths are based on atomic
physics and can be measured extremely accurately in a laboratory on Earth.

If a star is moving towards us, the whole pattern of the spectrum gets
shifted to shorter wavelengths, i.e. towards the blue end of the spectrum.
This is a BLUESHIFT, and we can measure it very accurately by comparing
the apparent wavelengths of the spectral lines with the known laboratory
wavelengths. If the star is receding, the pattern moves to longer, redder
wavelengths, and this is a REDSHIFT. "Blueshifts come, and redshifts go,
and that's pretty much everything you need to know."

Here's the equation:

v = c x (wavelength shift) / (wavelength)

where v is the relative velocity (speed) of the star, c is the velocity of
light, and {wavelength} the known wavelength of the line as measured in
the laboratory. We can use this equation until the relative speed becomes
a significant fraction of the speed of light -- and then it's back to
Einstein's Theory of Relativity, for a more detailed formula.

Extremely careful measurements of nearby stars can determine their
relative speeds with a precision as small as 10 meters per second.
Analyzing a large number of nearby stars shows that our Sun and its
neighbors orbit the distant center of our Milky Way galaxy with a velocity
of 250 km/sec. We're about 26,000 light years from the center of the
Galaxy, and so it'll take 220 million years for us to complete an orbit.
We can also tell that the stars nearer the center of the Galaxy rotate
faster, so we're being 'passed' by those stars nearer the center, and
'overtaking' those stars that orbit further from the center of the Galaxy;
this is the DIFFERENTIAL ROTATION of the Galaxy.

But that's not all

There are many more things we can learn using the Doppler Shift, and here
is a summary of just a few:

We can measure the masses of binary stars, by detecting the velocity
changes as they orbit around their common center of gravity, and combining
these velocities with the period of the orbit.

In the same way, we can look for evidence of massive planets in orbit
around other stars, by searching for the small velocity changes in the
central stars caused by their unseen planetary companions. This is not an
easy thing to do. For example, the Sun and Jupiter move around their
common center of gravity with a period of 11.86 years, and the variation
of the Sun's motion as seen from an observer outside the Solar System has
an amplitude of 12.5 meters per second as a result. Scientists at NASA and
many universities are conducting long-term projects to monitor stars for
low-amplitude periodic variations in velocity that may reveal such planets
to us.

We can detect the rotation of the Sun easily enough by following the
positions of SUNSPOTS, but the spectrum of the light from various regions
of the Sun also shows this rotation. The equator at the Sun's east limb is
approaching us at 2 km/sec, and the west limb is retreating from us at the
same speed. The same thing happens in other stars. They're further away,
so we can't study each edge of the star in the same way. However, we can
see that the absorption lines are BROADENED, or smeared out, by the
rotation. Some stars have equatorial speeds of 400 km/sec; if they spun
any faster, they would break up!

When we look at the spectra of other galaxies and map their
velocities, we find that on average, all galaxies are speeding away from
each other, with very high redshifts. (There are exceptions, where
galaxies are close enough to be drawn together by their gravities.) The
Doppler Shift tells us that the universe as a whole is expanding. What's
more, galaxies at greater distances ('higher redshifts') are speeding away
more quickly -- just as you'd expect in the aftermath of a giant
explosion: the Big Bang.
And finally, it now looks as if the expansion of the universe is accelerating.
Read more about the Hubble constant, the expansion of the universe, and dark energy

And so on, out to the edges of the Universe ... 'Behind' the stars
and galaxies and clusters of galaxies, scientists can detect the COSMIC
BACKGROUND RADIATION left over after the Big Bang. This radiation has a
temperature just three degrees above Absolute Zero -- redshifted into the
radio portion of the electromagnetic spectrum. Read more about the cosmic microwave
background.

So, using one simple physical phenomenon -- the Doppler Shift -- that you
can hear for yourself on any city street, scientists can make discoveries
about the speeds, masses and behavior of stars as close as our Sun or as
distant as other galaxies, and study the properties of those galaxies to
find out the structure of the Universe. Think of that, next time a fire
truck goes by!